Question

What is the formula for rotational force?

Answer 1

Torque is the measure of rotational force, defined by the formula T = Iα, where I is the moment of inertia and α is the angular acceleration. This formula is derived as an analogue to Newton's second law of motion (F = ma), applying to rotation.

Step-by-step explanation:

The concept of rotational force in physics refers to a quantity known as torque (T), which is the rotational equivalent of force. Newton's second law for rotation gives us the formula to calculate torque that is generated when a force is applied at a distance r from a pivot point, causing an object to rotate. The formula for torque (T) can be expressed as T = Iα, where I is the moment of inertia (I = mr² for a point mass) and α is the angular acceleration. Moment of inertia is a crucial concept in this context, as it represents the rotational inertia, indicating how difficult it is to change an object's rotational motion.

While deriving the equation for rotational dynamics, a force F applied perpendicularly to the radius r results in torque T = Fr. Multiplying both sides of the equation F = ma by r, and taking into account that linear acceleration a equals radial distance r times angular acceleration α (a = rα), we obtain rF = mr²α. This eventually simplifies to T = Iα, linking torque to moment of inertia and angular acceleration, and serving as the rotational analogue to Newton's second law.

Answer 2

Answer: The formula for rotational force, also known as torque, is:

Torque = Force x Perpendicular Distance from the point of application of force to the axis of rotation

This formula expresses the fact that torque depends on both the force applied and the distance between the point of application of force and the axis of rotation. The force should be perpendicular to the axis of rotation, otherwise, only the perpendicular component of the force will contribute to the torque.

Mathematically, torque is usually represented by the symbol "τ" (tau), force is represented by "F", and the perpendicular distance is represented by "r". Therefore, the formula can be written as:

τ = F x r

The unit of torque is the newton-meter (Nm) in the SI system of units. In the cgs system of units, the unit of torque is the dyne-centimeter (dyn-cm).

Step-by-step explanation: